Question

For whatever reason, the relaxation time of a conductor increases by a factor of 2 and the number of electrons per unit volume decreases by a factor of 3. Given all other factors remain the same, the new conductivity changes by what factor?

• A. $\frac{2}{3}$
• B. $\frac{3}{2}$
• C. $6$
• D. $\frac{1}{6}$

Answer 1

The correct option is A $\frac{2}{3}$

If you don’t remember the exact relation of conductivity, number density and relaxation time it’s cool, just remember that conductivity increases linearly with both number density (n) and relaxation time (τ). The relation is If relaxation time increases by 2 times, so does conductivity and if number density decreases by 3 times so does conductivity. So overall conductivity changes by a factor of $\frac{2}{3}$